Question

A firm has a proposed 5-year project. If accepted today (t=0), the project is expected to generate positive net cash flows for each of the following five years(t=1 through t=5). A new machine will be put in service, and to implement this project, an old machine will be sold. Note the following items. The new machine costs $1,000,000. Shipping and installation will cost an additional $500,000. Thus the Installed Cost is $1,500,000.This new machine will be sold five years from today when this project is completed. We believe that it can be sold for $100,000 in five years. If this project is accepted, then an old, fully depreciated, machine will be replaced. The old machine can be sold for $50,000 today. The Installed Cost of this new asset will be depreciated using the IRS 5-year MACRS schedule: year 1, 20%; year 2, 32%; year 3, 19.2%; year 4, 11.52%; year5, 11.52%; and year 6, 5.76%. Note that these yearly amounts sum to 100%. The project will increase revenues and operating expenses (before depreciation and amortization) by $800,000 and $300,000 per year, respectively, for each of the following five years (t=1 to t=5).

An initial increase in Net Working Capital of $50,000 is required today and this amount will be recovered in 5 years when the project is terminated. No other changes in NWC will be required during the project’s life. The cost of capital of the project is r=11%. The corporate income tax rate is 40%.

You are required to determine the following:

a) Compute the relevant cash flows

b) Compute the NPV, IRR , Payback period and profitability index to decide whether a firm

should start this project or not.

b) Compute the NPV, IRR , Payback period and profitability index to decide whether a firm

should start this project or not.

Answer 1

Cash outflow in year 0 = cost of new machine - sale of old machine + investment in NWC

Operating cash flow (OCF) each year = income after tax + depreciation

profit on sale of machine at end of year 5 = sale price - book value

book value = original cost - accumulated depreciation

after-tax salvage value = salvage value - tax on profit on sale of machine   

NPV and IRR are calculated using NPV and IRR functions in Excel

Payback period is the time taken for the cumulative cash flows to equal zero

Payback period = 3 + (cash flow required in year 4 for cumulative cash flows to equal zero / year 4 cash flow) = 3 + ($172,800 / $369,120) = 3.47 years

NPV is $129,282

IRR is 14.35%